At present steel framework based buildings are prevalent in civil engineering. Application of hollow section columns have proven to be efficient in low-rise buildings. In some cases frame joints of beam to column connections are needed in this kind of building structures. This paper considers rigid joints of I-beam to hollow section column connections allowing for an elastic pliability. The results of pliability estimation of these joints are represented for various construction solutions. Dependences are obtained for the relation of the support moment in a beam to its corresponding value in absolutely stiff connection on the rigidity of the joint. The dependence diagrams of rigidity of the joint on the parameters of its elements are obtained.